system simulation programs

Overview

A collection of standalone programs for simulating various properties of ensembles.

  • gen_sampling_err_table.f90

  • full_error.f90

  • obs_sampling_err.f90

  • sampling_error.f90

  • system_simulation.f90

  • test_sampling_err_table.f90

  • correl_error.f90

The program of most interest here is ``gen_sampling_err_table.f90`` which generates the lookup table needed when using sampling error correction in ``filter``. Talk to Jeff Anderson about the other programs in this directory.

To enable the sampling error correction algorithm in filter, set the namelist item &assim_tools_nml : sampling_error_correction to .true., and copy the netCDF file system_simulation/sampling_error_correction_table.nc into the run directory. The supported set of precomputed ensemble sizes can be found by exploring the ens_sizes variable in sampling_error_correction_table.nc. To add support for another ensemble size, build the executables in the work directory, (usually by running quickbuild.csh) set the ens_sizes (it takes a list, but keep it short) namelist item in work/input.nml, and run gen_sampling_err_table. It generates a LARGE number of samples per ensemble size for statistical rigor. Larger ensemble sizes take longer to generate, and compiler optimizations matter - perhaps significantly. For example, the numbers below come from calculating one ensemble size at a time on my desktop machine with gfortran and basic optimization:

ensemble size

run-time (seconds)

10

57

50

273

100

548

The basic structure of sampling_error_correction_table.nc is shown below.

0[1095] desktop:system_simulation/work % ncdump -v ens_sizes *nc
netcdf sampling_error_correction_table {
dimensions:
        bins = 200 ;
        ens_sizes = UNLIMITED ; // (40 currently)
variables:
        int count(ens_sizes, bins) ;
                count:description = "number of samples in each bin" ;
        double true_corr_mean(ens_sizes, bins) ;
        double alpha(ens_sizes, bins) ;
                alpha:description = "sampling error correction factors" ;
        int ens_sizes(ens_sizes) ;
                ens_sizes:description = "ensemble size used for calculation" ;

// global attributes:
                :num_samples = 100000000 ;
                :title = "Sampling Error Corrections for fixed ensemble sizes." ;
                :reference = "Anderson, J., 2012: Localization and Sampling Error
                              Correction in Ensemble Kalman Filter Data Assimilation.
                              Mon. Wea. Rev., 140, 2359-2371, doi: 10.1175/MWR-D-11-00013.1." ;
                :version = "" ;
data:

These ensemble sizes are already supported!
 ens_sizes = 5,  6,  7,  8,  9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 44,
            48, 49, 50, 52, 56, 60, 64, 70, 72, 80, 84, 88, 90, 96, 100, 120, 140, 160, 180, 200
}

Namelist

This namelist is read from the file input.nml. Namelists start with an ampersand ‘&’ and terminate with a slash ‘/’. Character strings that contain a ‘/’ must be enclosed in quotes to prevent them from prematurely terminating the namelist.

&gen_sampling_error_table_nml
   ens_sizes = 5,  6,  7,  8,  9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 44,
              48, 49, 50, 52, 56, 60, 64, 70, 72, 80, 84, 88, 90, 96, 100, 120, 140, 160, 180, 200
   debug = .false.
   /

Item

Type

Description

ens_sizes

integer(200)

An array of ensemble sizes to compute. Any new size gets appended to the variables in the netCDF file. Any order is fine, the array does not have to be monotonic. The numbers listed in the example exist in the file distributed with DART. Do not get carried away by generating a lot of new ensemble sizes in one execution. The table of run-time above should give you some indication of how long it takes to create a new entry.

debug

logical

A switch to add some run-time output. Generally not needed.

Modules used

types_mod
utilities_mod
random_seq_mod

  • input.nml for the run-time input

  • sampling_error_correction_table.nc is both read and written. Any new ensemble sizes are simply appended to the file.

  • dart_log.out has the run-time output.

  • input.nml for the run-time input

  • final_full.N are created - N is the ensemble size.

  • dart_log.out has the run-time output.

References

  • Anderson, J. L., 2012: Localization and Sampling Error Correction in Ensemble Kalman Filter Data Assimilation. Mon. Wea. Rev., 140, 2359-2371 doi: 10.1175/MWR-D-11-00013.1